Recently rebranded as the Carabao Cup, City are bidding to win the competition for the fifth time.
They last lifted the trophy in 2016 after a dramatic penalty shoot-out win over Liverpool at Wembley.
The game will be played at The Hawthorns on the week beginning 18 September, with the exact time and date yet to be confirmed.
Keep an eye on mancity.com for further details in the coming days.
Full Third Round draw:
West Brom v Man City
Everton v Sunderland
Leicester v Liverpool
Manchester United v Burton Albion
Brentford v Norwich City
Wolves v Bristol Rovers
Burnley v Leeds United
Arsenal v Doncaster Rovers
Bristol City v Stoke City
Reading v Swansea City
Aston Villa v Middlesbrough
Chelsea v Nottingham Forest
West Ham v Bolton
Crystal Palace v Huddersfield Town
Tottenham Hotspur v Barnsley or Derby County
Bournemouth v Brighton